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An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves by Dr. T.E. Venkata Balaji, Department of Mathematics, IIT Madras. For more details on NPTEL visit http://www.nptel.iitm.ac.in/syllabus/111106044/

Goals of Lecture 14:

* In the previous lecture, the universal covering space was constructed for a given space as a Hausdorff topological space along with a natural map into the given space. In this lecture, we show that this natural map is a covering map

* It would follow that if the given space is locally arcwise connected and locally simply connected, then the same properties hold
for the universal covering space as well

Keywords for Lecture 14:

Path, Fixed-end-point (FEP) homotopy equivalence class, fundamental group, pathwise or arcwise connected, Hausdorff, locally simply connected, universal covering, basic open set, base for a topology, sub-base for a topology, admissible neighborhood